The present invention relates to techniques used in data communications for mitigating the effects of crosstalk in communications channels.
Crosstalk is the unintentional coupling of signals in a communications system. In many communications systems, crosstalk is a significant impediment to reliable transmission. For example, telephone service to the home is typically provided over a simple `twisted pair` of wires, often referred to as a `loop`. A particular customer's loop is typically bundled with loops of other nearby customers in a common cable. The proximity of the loops within the cable results in electromagnetic coupling between the loops. If the coupling is sufficiently strong, it is possible for the voice signals on one user's loop to interfere with the intelligibility of conversations on other users' loops.
The degree of coupling between loop pairs within the cable increases with frequency, and generally speaking, at the low frequencies used for voice transmission, objectionable crosstalk between telephone loops is not a significant problem. Even modems which transmit data using signals in the voice-frequency band (at rates up to approximately 24 kbps) are not seriously affected by cable crosstalk. However, there are several applications presently under consideration for which unloaded bundled telephone loops or other twisted-pair cables would be used to provide megabit-per-second (and higher) data transport. At the high signaling rates necessary for these applications, crosstalk is the dominant impairment to reliable transmission.
Data signals generated by many commonly employed forms of linear modulation are known as cyclostationary signals. For example, see "Exploitation of Spectral Redundancy in Cyclostationary Signals, W. A. Gardner, IEEE Signal Processing Magazine, vol. 8, no. 2, pp. 14-36, April 1991. Thus, assuming such modulation techniques are used in the applications mentioned above, both the desired data signal and the crosstalk signals are cyclostationary. It has been realized that the effects of crosstalk among mutually interfering cyclostationary signals can be reduced by employing an adaptive fractionally-spaced equalizer (FSE) at the data receiver. For example, see "Minimum Mean-Square Equalization in Cyclostationary and Stationary Interference Analysis and Subscriber-Line Calculations," B. R. Petersen and D. D. Falconer, IEEE J. on Select. Areas Commun., August 1991; "Equalization in Cyclostationary Interference", B. R. Petersen, Ph.D. thesis, Oct. 31, 1991, Carleton University, Ottawa, Canada. The degree to which an FSE can mitigate the crosstalk depends strongly on the spectral relationships between the desired signal and the crosstalk signal at the input to the FSE; these spectral relationships in turn depend on the spectra of the transmitters. Furtherefore, for reasons of practical simplicity, it is desirable to impose the constraint that each transmitter use the same shaping function. Consequently, an important practical issue for these applications is to determine the particular transmitter spectral shaping function to be used for a given channel. For example, see "Suppression of Nearand Far-End Crosstalk by Linear Pre- and Post-Filtering", M. L. Honig, P. Crespo, and K. Steiglitz, IEEE J. on Select. Areas Commun., April 1992.
For the `classical` linear communications channel in which only noise, but not crosstalk, is present, the optimum transmitter shaping function under the minimum mean-squared error (MMSE) criterion has Nyquist spectral support. However, it is generally appreciated that the optimum MMSE transmitter for mitigation of crosstalk under the above constraints requires a transmitted spectral support greater than the Nyquist rate. This type of transmitter will be referred to as an `extended bandwidth` (EBW) transmitter. Unfortunately, analyses and simulations of crosstalk systems in the known prior art have provided no known general solution to the design of the spectral shapes for EBW transmitters which realize the near-optimum performance that is theoretically possible.